# Options Degenerate Marketplaces (Part 2)

So, it’s been a while. This month has been quite surreal. It’s a bit difficult to focus on schoolwork and writing itself when stuff like this happens:

So this part, the ending part of Options Degenerate Marketplaces, was a bit delayed. Similarly, I did not expect that in the interim, the concept of options dominance and NOPE itself would blow up so heavily.

In the first part, we discussed simply the concept of **options dominance, **or a market state — which we find ourselves in — which the weight of the options market (measured of course in the hedge ratio, delta) is a substantial or majority fraction of the underlying’s liquidity. Since liquidity as a word is the analyst or management consultant of the finance world, for this article let’s fix the term to mean **market impact**, or the change in price of an asset caused by trading it. In a very illiquid market, we expect that buying or selling an asset will change the price of it a whole lot; in a very liquid market, this is the opposite (for a deeper understanding here, check out my post A Story of Volatility, Liquidity, and Returns).

In this part, let’s delve deeper into how options are creating illiquidity, and what this means for the state of the market.

# Queen Delta

In general, delta ends up being the least sexiest of all the major Greeks (we don’t talk about rho, no one talks about rho).

Delta, as I’ve discussed in my deep dive on the Greeks in Gamestop: Power to the Players, Part 2 represents many things:

- In Black-Scholesland, delta represents the instantaneous rate of change of the option price versus the underlying price (e.g. a 50 delta option will move $.50 in response to a $1 move int he underlying).
- It roughly approximates the chance a given option ends up in-the-money (hence why an at-the-money option has 50 delta, or 50% chance).
- It represents the
**hedge ratio**, or the amount of shares one must buy/short to offset the market position of holding the option.

In general, delta isn’t that interesting in most applications because it tends to represent a static state in time, rather than reflect the true dynamism of the market. In fact, delta is more of a mathematical formalism as a hedging ratio, because it’s only the ‘true’ value at instantaneous scales. In general, its derivatives (e.g. gamma, vanna) tend to get more press and attention since those reflect the dynamic state of delta — where the market **will** be, rather than where it is now.

However, at the end of the day, delta is the link between an option and the underlying, due to this nifty concept called **leverage.** The hedging ratio, delta, can be thought of as the number of shares needed to successfully hedge out the cost of the option (for the seller), but can also be viewed as a measure of the leverage. This is often described (in terms of price effect) as **lambda**, which is simply the delta of an option multiplied by the **gearing factor**, which is the ratio of the option price to the underlying price.

More succinctly, we can describe the option’s delta as representing a position in the underlying equating to an equal number of shares (so a 22 delta position represents 22 shares, for example).

This is the key to why delta is important. We can’t simply imagine the options market as disconnected from the underlying market, because the options market **is** the underlying market. While certainly not a one to one ratio (especially on tickers like SPY, which can be hedged in many different ways), you can understand the ‘weight’ of the options market on the underlying in terms of delta.

Interestingly, because of the parity of puts and calls, we can construct a delta neutral (delta = 0) position using a long put and long call in the underlying. This should come as no surprise to most experienced traders, since this allows us to construct the **straddle** position, and lets us benefit from changes in the asset pricing without having a directional bias.

Given a straddle is essentially a flat position at a certain price, it follows logically that to hedge this position requires no shares to be bought or sold. Assuming an idealized scenario, this implies at time t, price S for a straddle position on S, the counter-party (a market maker, usually) would have not have to hedge the position (e.g. buying/shorting shares in the underlying) and therefore have no price impact on the underlying (per the discussed argument in Part 1).

From this, we can surmise that call delta and put delta at any given interval of time act much like a weighing scale, balancing each other out. This is implied by the reciprocal signage between calls and puts, but has real world implications on price. If the delta implied by put options and call options is equal, at a given time t, price S we would anticipate no ‘weight’ felt in either direction on the underlying market. In practice, this is woefully insufficient for measuring reality due to second-order effects (e.g. gamma, vanna, charm) which do not allow us to neatly assume all deltas weigh future price or time movement equally.

However, this does give us an abstract measure of options dominance, at least in the bluntest sense. Options dominance can be stated simply as the measure of total shares used to hedge the options market in the underlying versus the total shares moved in the underlying market. In reality this tends to be an insufficient measure, but a fairly robust one.

This is why delta is queen. Despite being boring and static, much like the passive investing, options by design have to draw liquidity out of the underlying market to be rationally priced. This draw is a function of the underlying delta.

# Volatility and Declining Liquidity

In recent years, many market practitioners and theorists have rightfully warned of the passive investing bubble. Logically speaking, passive investing into popular ETFs has a distortion effect on price formation in three ways:

**Redemption/Creation**— Despite popular belief a float-cap-weighted ETF like SPY in general does not substantially impacts price formation of its basket on the day to day by itself. This is fairly intuitive why — as the price of components rise and fall, their weighting in the index rises and falls with it. This means for example, if my index consists of 100 shares of Tesla which comprises 20% of my index, it should — assuming Tesla drops in value — drop as a percentage of my total index’s weight. However, this will not actually cause the buying or selling of any shares by itself. This price distortion can occur via the creation/redemption process of ETFs, illustrated below:

The process of creation and redemption is critical to the proper functioning of an ETF, which is designed to track its net asset value (NAV), or the value of its component basket. As the ETF trades, it can briefly trade above or below its NAV, and the action of authorized participants (arbitrageurs) can bring it back into line. This **does** have predictable price distortion effects, given its impact on supply and demand for the component stocks.

2. **Rebalancing** — This is a dominant price distortion effect in non-floating ETFs, such as the popular RSP (Invesco S&P 500® Equal Weight ETF). Unlike a floating index like SPY, where index weightings are allowed to float, in an equal weighting index there is a necessity to consistently rebalance holdings in order to retain equal weighting and meet fund objectives. This net causes the buying and selling of shares at mechanical intervals, leading to price distortion effects.

3. **Reduced Liquidity** — Here’s my favorite one, and the most salient to Options Degenerate Marketplaces. Much like the leverage implied by Queen Delta, ETFs in essence represent shares ‘locked’ away from the normal market, “hedging” the ETF’s exposure from directional risk when its holdings’ values fluctuate. This naturally reduces the float of its holdings, which similarly reduces the potential market depth for its holdings, making each “natural” (e.g. non-mechanical) buy or sell have a larger impact on the underlying price.

As we discussed in A Story of Volatility, Liquidity, and Returns, there is a deep connection between volatility and liquidity (again, referenced here as market depth) — as liquidity decreases, volatility increases, and vice versa. As markets get shallower, we see each natural buy and sell matter more on determining price formation, increasing volatility (and due to the relationship between volatility and returns, higher expected returns).

What’s interesting however, is that the ETF component here is — especially in case 3 — fairly readily measurable by market participants. It doesn’t take much more than a spreadsheet to determine how many shares of a stock are spoken for by the ETFs that own it. Further, one could — assuming a large amount of time and patience — build a model to account for rebalancing in most cases, given a deep dive into fund prospectuses. Similarly, with more patience one could largely track creation and redemption in real time as a function of how far the ETF strays from net asset value.

What tends to be more insidious over time, and the cause of the **degenerate marketplace** is the conditions of dynamic liquidity absorption — the liquidity spoken for by Queen Delta. Unlike the ETF conditions described above, options represent an **implied illiquidity** factor, given that they show up in the order book and trade as normal shares. Given the dynamism of the options market and the convexity of positions, the shares belonging to Queen Delta change hands rapidly as part of the normal trading volume. But unlike a natural buy and sell order, these shares are spoken for, traded mechanically according to the cold mathematical formalism of option pricing models. As the underlying goes up, so does Queen Delta (in a call skew). The delta weight magnifies the effects of the normal price formation, distorting it without a trace.

**Options Degeneracy**

A long time ago, people supported the introduction of options as a way to *reduce* volatility, with the tacit understanding that it should stabilize price by allowing market participants to hedge positions and reduce uncertainty. However, in the degenerate case as described above, when a substantial fraction of the market is implicitly controlled by Queen Delta, they tend to **magnify** volatility.

This is simple to understand —when options are hedged in the underlying, as per Part 1 we can expect the price to move slightly further in either direction depending on the weight of the call and put delta distributions. This is because the net delta effectively magnifies the price impact of any transaction in the underlying due to hedging demands (e.g. the second order derivatives).

When options are a small fraction of the underlying market, they tend to stabilize the underlying by reducing net directional exposure. However, when options reach a state where they imply via delta a large or majority fraction of the underlying liquidity, they tend to increase sensitivity to perturbation (e.g. negative catalysts, Jewish holidays, Elon tweeting). This is a fantastic environment for the volatility trader, but a much less fantastic environment for Grandma’s 401k.

# Conclusions

I tend to have a bad rap for predicting crashes, partially warranted by my bearish inclinations, partially due to NOPE’s association with correction periods. One of the major questions I had when starting to observe NOPE was simply “Why does high end of day readings tend to associate with correction periods, either tops or bottoms?”

To the clever reader, per the above they may have already guessed the answer. To the rest of us, it is simple — sensitivity to perturbation. The magnitude of NOPE simply reflects some idealized notion of the shadow illiquidity of the options market, and a high value reflects a state sensitivity to perturbation. NOPE is responsible for a selloff or bounce not because of any preternatural effects (even though I would love to be a witch) — it is simply because the market is more sensitive to small perturbations. When a selloff occurs, it isn’t because of some magical end-of-day reading; there is always a root cause, usually found retrospectively. If we consider the market to be an endless forest and the current state to be a forest in drought, NOPE is simply its barometer. No amount of dead trees on the floor will cause a fire. There’s always a match.